For \(n=2\)  the same argument works with the same ODE system (REF ).
In fact, this system for \(n=2\)  was already indicated by Douglas, and in [1]}
the \(3\times 3\)  matrix \(\Delta \)  is nondegenerate, implying \(\phi _{ij}=0\)  as the only solution.
Our observation extends his result without going into detailed analysis of solvability of the
fundamental system.
